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  • Solve this problem The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :

 The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :

 

  • Option 1)

    \frac{1}{2}

  • Option 2)

    \frac{2}{\sqrt{5}}

  • Option 3)

    \frac{\sqrt{3}}{2}

  • Option 4)

    \frac{\sqrt{3}}{4}

 

Answers (1)

best_answer

As we learnt in

Eccentricity -

e= \sqrt{1-\frac{b^{2}}{a^{2}}}

- wherein

For the ellipse  

\frac{x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}= 1

It passes through (4,-1) and (-2,2)

\frac{16}{a^{2}}+\frac{1}{b^{2}}=1

and  \frac{4}{a^{2}}+\frac{4}{b^{2}}=1\left.\begin{matrix} & \end{matrix}\right\}\times 4

\frac{15}{b^{2}}=3=>b^{2}=5

\frac{4}{a^{2}}+\frac{4}{5}=1

a^{2}=20

e=\sqrt{1-\frac{b^{2}}{a^{2}}}=\sqrt{1-\frac{5}{20}}=\frac{\sqrt{3}}{2}


Option 1)

\frac{1}{2}

This option is incorrect

Option 2)

\frac{2}{\sqrt{5}}

This option is incorrect

Option 3)

\frac{\sqrt{3}}{2}

This option is correct

Option 4)

\frac{\sqrt{3}}{4}

This option is incorrect

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Plabita

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